$1.$ Consider the rigid frame and loading shown in the figure below. Assume EI is constant. $(20$ points total$)$

$($a$)$ What is the minimum number of points of inflection $($P$.$O$.$I.$)$ needed to convert this indeterminate frame into a version that can be analyzed using approximate methods? $(5$ points$)$

$($b$)$ Draw a reasonable guess$-$timate of the deflected shape of the frame, and indicate a reasonable location for each point of inflection $($P$.$O$.$I.$)$ you believe is needed. Provide some words of explanation for why you drew the deflection of the beam the way you drew it$.$ For each P$.$O$.$I. in that figure, calculate its location away from an appropriate support and indicate that distance on your figure. $(5$ points$)$

$($c$)$ Calculate the reactions at supports A and B using what you know must be true at a point of inflection. $(10$ points$)$